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Computational Methods for Reinforced Concrete Structures

  • ID: 2755184
  • Book
  • 354 Pages
  • John Wiley and Sons Ltd
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The book covers the application of numerical methods to reinforced concrete structures. To analyze reinforced concrete structures linear elastic theories are inadequate because of cracking, bond and the nonlinear and time dependent behavior of both concrete and reinforcement. These effects have to be considered for a realistic assessment of the behavior of reinforced concrete structures with respect to ultimate limit states and serviceability limit states.

The book gives a compact review of finite element and other numerical methods. The key to these methods is through a proper description of material behavior. Thus, the book summarizes the essential material properties of concrete and reinforcement and their interaction through bond. These basics are applied to different structural types such as bars, beams, strut and tie models, plates, slabs and shells. This includes prestressing of structures, cracking, nonlinear stressstrain relations, creeping, shrinkage and temperature changes.

Appropriate methods are developed for each structural type. Large displacement and dynamic problems are treated as well as short–term quasi–static problems and long–term transient problems like creep and shrinkage. Most problems are illustrated by examples which are solved by the program package ConFem, based on the freely available Python programming language. The ConFem source code together with the problem data is available under open source rules at concrete–fem.com.

The author aims to demonstrate the potential and the limitations of numerical methods for simulation of reinforced concrete structures, addressing students, teachers, researchers and designing and checking engineers.

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1 FINITE ELEMENTS OVERVIEW

Modeling Basics

Discretization Outline

Elements

Material Behavior

Weak Equilibrium and Spatial Discretization

Numerical Integration and Solution Methods for Algebraic Systems

Convergence

2 UNIAXIAL STRUCTURAL CONCRETE BEHAVIOR

Scales and Short–Term Stress–Strain Behavior of Homogenized Concrete

Long–Term Behavior –

Creep and Imposed Strains

Reinforcing Steel Stress–Strain Behavior

Bond between Concrete and Reinforcing Steel

The Smeared Crack Model

The Reinforced Tension Bar

Tension Stiffening of Reinforced Tension Bar

3 STRUCTURAL BEAMS AND FRAMES

Cross–Sectional Behavior

1 Kinematics –

2 Linear Elastic Behavior –

3 Cracked Reinforced Concrete Behavior –

4 Compressive Zone and Internal Forces –

5 Linear Concrete Compressive Behavior with Reinforcement –

6 Nonlinear Behavior of Concrete and Reinforcement

Equilibrium of Beams

Finite Element Types for Plane Beams

1 Basics –

2 Finite Elements for the Bernoulli Beam –

3 Finite Elements for the Timoshenko Beam –

4 System Building and Solution Methods –

5 Elementwise Integration –

6 Transformation and Assemblage –

7 Kinematic Boundary Conditions and Solution

Further Aspects of Reinforced Concrete

1 Creep –

2 Temperature and Shrinkage –

3 Tension Stiffening –

4 Shear Stiffness for Reinforced Cracked Concrete Sections

Prestressing

Large Deformations and Second–Order Analysis

Dynamics of Beams

4 STRUT–AND–TIE MODELS

Elastic Plate Solutions

Modeling

Solution Methods for Trusses

Rigid–Plastic Truss Models

More Application Aspects

5 MULTIAXIAL CONCRETE MATERIAL BEHAVIOR

Basics

1 Continua and Scales –

2 Characteristics of Concrete Behavior

Continuum Mechanics

1 Displacements and Strains –

2 Stresses and Material Laws –

3 Coordinate Transformations and Principal States

Isotropy, Linearity, and Orthotropy

1 Isotropy and Linear Elasticity –

2 Orthotropy –

3 Plane Stress and Strain

Nonlinear Material Behavior

1 Tangential Stiffness –

2 Principal Stress Space and Isotropic Strength –

3 Strength of Concrete –

4 Phenomenological Approach for the Biaxial Anisotropic Stress–Strain Behavior

Isotropic Plasticity

1 A Framework for Multiaxial Elastoplasticity –

2 Pressure–Dependent Yield Functions

Isotropic Damage

Multiaxial Crack Modeling

1 Basic Concepts of Crack Modeling –

2 Multiaxial Smeared Crack Model

The Microplane Model

Localization and Regularization

1 Mesh Dependency –

2 Regularization –

3 Gradient Damage

General Requirements for Material Laws

6 PLATES

Lower Bound Limit Analysis

1 The General Approach –

2 Reinforced Concrete Contributions –

3 A Design Approach

Crack Modeling

Linear Stress–Strain Relations with Cracking

2D Modeling of Reinforcement and Bond

Embedded Reinforcement

7 SLABS

A Placement

Cross–Sectional Behavior

1 Kinematic and Kinetic Basics –

2 Linear Elastic Behavior –

3 Reinforced Cracked Sections

Equilibrium of Slabs

1 Strong Equilibrium –

2 Weak Equilibrium –

3 Decoupling

Structural Slab Elements

1 Area Coordinates –

2 A Triangular Kirchhoff Slab Element

System Building and Solution Methods

Lower Bound Limit Analysis

1 General Approach and Principal Moments –

2 Design Approach for Bending –

3 Design

Approach for Shear

Kirchhof Slabs with Nonlinear Material Behavior

8 SHELLS

Approximation of Geometry and Displacements

Approximation of Deformations

Shell Stresses and Material Laws

System Building

Slabs and Beams as a Special Case

Locking

Reinforced Concrete Shells

1 The Layer Model –

2 Slabs as Special Case –

3 The Plastic Approach

9 RANDOMNESS AND RELIABILITY

Basics of Uncertainty and Randomness

Failure Probability

Design and Safety Factors

10 APPENDICES

A Solution of Nonlinear Algebraic Equation Systems

B Crack Width Estimation

C Transformations of Coordinate Systems

D Regression Analysis

E Reliability with Multivariate Random Variables

F Programs and Example Data

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Ulrich Häußler–Combe
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